Simplifying Radical Expressions Calculator Cube Root

How to Use This Calculator

Enter the radical expression you want to simplify in the input field. The calculator will:

1. Identify the radicand and any perfect square factors
2. Factor out the largest perfect square
3. Simplify the remaining radical
4. Display the simplified form

For cube roots, the calculator will identify perfect cubes and simplify accordingly. The result will show both the simplified form and the original expression for comparison.

Simplifying Radical Expressions

Radical expressions can often be simplified by factoring out perfect squares from the radicand. The general rule is:

For example, to simplify √72:

1. Factor 72: 72 = 36 × 2
2. √72 = √(36 × 2) = √36 × √2 = 6√2

The calculator performs these steps automatically for any input you provide.

Working with Cube Roots

Cube roots can be simplified by factoring out perfect cubes. The general rule is:

For example, to simplify ³√108:

1. Factor 108: 108 = 27 × 4
2. ³√108 = ³√(27 × 4) = ³√27 × ³√4 = 3√4

The calculator handles cube roots similarly to square roots, identifying perfect cubes and simplifying accordingly.

Worked Examples

Example 1: Simplifying √128

1. Factor 128: 128 = 64 × 2
2. √128 = √(64 × 2) = √64 × √2 = 8√2

Example 2: Simplifying ³√500

1. Factor 500: 500 = 125 × 4
2. ³√500 = ³√(125 × 4) = ³√125 × ³√4 = 5√4

Example 3: Simplifying √(x² + 2x + 1)

1. Recognize the perfect square trinomial: x² + 2x + 1 = (x + 1)²
2. √(x² + 2x + 1) = √(x + 1)² = x + 1 (for x ≥ -1)